Two-Variable Data: Models and Scatterplots Flashcards

A linear model for daily temperature (x, °F) and swimming pool attendance (y, people) is y = 5x − 150. On what temperature day does attendance equal 100 people?

Answer: 50°F

Set 100 = 5x−150 → 5x=250 → x=50.

Data shows sales (y) in thousands grow as y = 8(1.2)^x. After 3 years (x=3), what are predicted sales?

Answer: 13.824 thousand

y = 8(1.2)^3 = 8 × 1.728 = 13.824 thousand.

In a scatterplot, a point has a large positive residual. What does this mean?

Answer: The actual y value is much higher than the model predicted.

Residual = actual y − predicted y; a large positive residual means actual y >> predicted y.

The line of best fit for data on advertising (x, $000) and revenue (y, $000) passes through (2, 50) and (8, 80). What is the slope?

Answer: 5

Slope = (80−50)/(8−2) = 30/6 = 5.

A model y = kx² fits a dataset. When x = 3, y = 36. What is the value of k?

Answer: 4

36 = k(9) → k = 36/9 = 4.

A scatterplot of income (x) and spending (y) has a line of best fit y = 0.75x + 500. A household earns $4,000. What does the model predict for spending?

Answer: $3,500

y = 0.75(4000)+500 = 3000+500 = 3500.

A scatterplot shows data with no discernible pattern — points are randomly scattered. What is the approximate value of r?

Answer: r ≈ 0

No pattern in a scatterplot corresponds to little or no linear association, so r ≈ 0.